Not to try to temper your frustration (which is quite legitimate), but in this context, "we're looking for a different skill set" is almost certainly a foil. Quite often companies will say things like that when really they mean they were just fundamentally disappointed in you for reasons X or Y they would find too awkward or risky to disclose to you.
Have to agree here. If you got to the onsite interview then there is a high likelyhood they thought there might be a fit.
This has been discussed before but basically telling a candidate that you passed on them for a specific reason is seen as an invitation to argue the point, so people say something like 'wrong skill set.' Easier just to move along and not worry about it too much.
